The conceit is that there are four relatively distinct regions that divide the campaign wold into four equal quadrants; each serves as the sandbox for games run by one of the four DMs, with players running their characters in the multiple regions.

I placed a megadungeon in each region close to the center of the map so dudes from different regions could easily access them.

I tried something like this with my last AD&D campaign, as much to give myself a chance to play as to expand the campaign world and player group... the off-week DM (who was a player when I was DMing) kept doing things in his part of the world that conflicted with how the main campaign was unfolding.

Add that to other multi-DM attempts years earlier, and in hindsight I have to say you're better off running separate campaigns - and if there is any crossover, make it something like dimensional travel between alternate worlds.

This from someone who really enjoys the crossover episodes of the new Doctor Who and its two spinoff series :)